Graham's Number, the best known upper bound for a problem in Ramsey theory, is listed in the Guiness Book of World Records as "the highest number ever used in a mathematical proof." The number, originating in a 1971 paper by Graham and B.L. Rothschild, cannot be expressed in conventional notation; Donald Knuth's arrow notation, invented in 1976, is necessary. As of 2003, the best known lower bound for this problem is 11.